Electron vortices in semiconductors devices

Abstract

The hydrodynamic model of electron transport in semiconductors is analyzed and, in analogy with vortices in fluid mechanics, the curl of electron velocity is defined as electron vorticity, and the transport equation for the electron vorticity is derived. Aside from the classical hydrodynamic sources of vorticity, collision terms in the continuity and momentum equations are identified as sources and sinks of electron vorticity. Similar to three-dimensional fluid flows there is a vortex stretching term in the vorticity equation. This term could be responsible for the possible cascade of electron kinetic energy to small scales and formation of chaotic turbulent electron transport regimes. A scale analysis of the electron vorticity equation is performed and the relative order of magnitude of each sources of vorticity is found. This analysis and the calculation of electron mean-free-path due to electron–electron and electron–phonon scatterings characterize a transport regime with significant electron vorticity effects. Furthermore, conditions for observation of electron vortices in semiconductor devices are predicted.